The canonical decomposition of once-punctured torus bundles

  • Marc Lackenby

    Oxford University, UK


We determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure and that is invariant under a certain involution is the ideal triangulation defined by Floyd and Hatcher. Unlike previous work on this problem, the techniques we use are not geometric. Instead, they involve angled polyhedral decompositions, thin position and a version of almost normal surface theory.

Cite this article

Marc Lackenby, The canonical decomposition of once-punctured torus bundles. Comment. Math. Helv. 78 (2003), no. 2, pp. 363–384

DOI 10.1007/S000140300015